minimum detectable concentration and concentration
TRANSCRIPT
PNNL-25418
Prepared for the U.S. Department of Energy under Contract DE-AC05-76RL01830
Minimum Detectable Concentration and Concentration Calculations
Matthew W Cooper James H Ely James C Hayes Justin I McIntyre Brian T Schrom
May 2016
2
Minimum Detectable Concentration and Concentration Calculations
Matthew W. Cooper James H. Ely James C. Hayes Justin I. McIntyre Brian T. Schrom
May 2016
Prepared for the U.S. Department of Energy
under Contract DE-AC06-76RL01830
3
DISCLAIMER
This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor Battelle Memorial Institute, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or Battelle Memorial Institute. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.
PACIFIC NORTHWEST NATIONAL LABORATORY
Operated by
BATTELLE
For the
UNITED STATES DEPARTMENT OF ENERGY
Under Contract DE-AC05-76RL01830
4
Contents
Executive Summary ............................................................................................................................ 5 Concentrations, Uncertainties and MDC ............................................................................................ 6 Regions of Interest (ROI) .................................................................................................................... 8 LC Calculation .................................................................................................................................. 10 Specific Cases ................................................................................................................................... 16
135Xe .................................................................................................................................. 16 133Xe .................................................................................................................................. 17 131mXe ................................................................................................................................ 19
Conclusion ........................................................................................................................................ 20
Figures
Figure 1: The detection limit for a specific radioactivity measurement process is plotted in increasing order. LC, LD, and LQ are the critical level, detection limit, and determination limit as described is Currie (1968). ............................................................. 6
Figure 2: Placement of the 7 regions of interest (ROI). ..................................................................... 8 Figure 3: A radon spike used to determine interference ratios with the ROI’s overlaid. ................... 9 Figure 4: 135Xe spike used for determination of 133Xe ROI ratios with ROI’s overlaid. The upper
right figure is an expanded view of the lower left section. ............................................... 10 Figure 5: A gas background after a medical isotope (133Xe, 131mXe) spike with ROI’s overlaid. .... 11 Figure 6: An example of a detector background data set with ROI’s overlaid. ............................... 11 Figure 7: Shows the chemistry timeline (vertical colored bands), detector acquisition (top
timeline), and an example of the isotope activity (given by the four lines in the bottom of the figure) present in a typical radioxenon system. In currently developed systems the measurement is corrected to a To of collection stop. The detector background (the section marked with a green horizontal bar) is the first data collected, which on this scale is too small to be displayed. The four regions: white, orange, yellow, and light blue show the number of decays at a given time. The white region (background) contains only decays from the ambient background and gas background (memory effect). The orange region (collection) assumes a linear increase in the number on radioxenon present, so there are an increasing number of decays as one goes forward in time. The yellow region (processing) represents the time between collection and data acquisition, so there is no added radioxenon and only decay. In the last region, light blue (acquisition), there is only decay of the radioxenon present. The top timeline shows what stage of acquisition the detector is in during any given chemistry stage of the system. ........................................................................................................................ 13
Figure 8: A sample file in which 135Xe is present. ........................................................................... 16 Figure 9: A sample file in which 133Xe is present. ......................................................................... 17 Figure 10: A sample file in which 131mXe is present. .................................................................... 19
5
Executive Summary This report highlights the work that has been completed on concentration calculations, uncertainties and minimum detectable concentration (MDC) for radioxenon collection systems. A discussion on the theory behind MDC calculations is given. In addition, regions of interest (ROI) and their role in correcting for both memory effects and interference terms are given in detail. A detailed derivation and walkthrough of the calculation is given with some discussion at each stage of the equation. Finally, some specific examples are given with typical numbers from an ARSA system as a guide.
IMS radionuclide stations, similar to the Automated Radioxenon Sampler/Analyzer (ARSA) developed at Pacific Northwest National Laboratory (PNNL), separate xenon gas from the sample collected. It uses a β-γ coincidence detection system to determine xenon concentrations. This report describes the procedure used to determine the concentration, the concentration uncertainties and the minimum detectable concentration (MDC) levels for each of the radioxenon isotopes of interest. All of these calculations require knowledge of the ambient background, interference terms, background due to residual gas (memory effect), detection efficiencies, branching ratios, collection time, processing time, and acquisition time. In addition, there are terms and uncertainties that could be added to the calculations but have been omitted by choice. These omissions have been highlighted for the sake of completeness.
6
Concentrations, Uncertainties and MDC The concentrations of radioxenon are very important for the detection of nuclear explosions. In addition, the propagation of the uncertainties, both statistical and systematic, gives a measure of the confidence that one has in the concentrations measured. Finally, the MDC indicates what the combined collection and detection systems should be able to see in the absence of any actual radioxenon isotopes (i.e. the system fidelity). For some locations, such as islands in the southern hemisphere, the MDC may be the only reported measurement made on a daily basis during long periods of non-testing. As the MDC is the most difficult to understand and calculate we begin with a general description of the calculations given by Currie (1968). Essentially, there are three limits: critical level (LC), detection limit (LD) and determination limit (LQ). These three limits can be visualized in (1) (Currie 1968).
Figure 1: The detection limit for a specific radioactivity measurement process is plotted in increasing order. LC, LD, and LQ are the critical level, detection limit, and determination limit as described is Currie (1968).
oC kL σα= (1)
DCD kLL σβ+= (2)
Where kα and kβ are the abscissa of the standardized normal distribution, with α (β) corresponding to the
probability of false positive (negative) events. For this report %5== βα . Since 2oDD L σσ += , the
detection limit can be rewritten as
2oDCD LkLL σβ ++=
(3)
After expanding and solving for LD one gets
7
++++= 22
2
24411
αβββ kk
LkLkLL CC
CD
(4)
Since βα kk = , (4) is simplified to
22 kLL CD += (5)
After substituting (1) into (5)
oD kkL σ22 += (6)
In the case where 645.1=k
oDL σ65.471.2 += (7)
Where,
222MemoryCntceCntInterferenBckCnto MemoryCntceCntInterferenBckCnt σσσσ +++++=
(8)
The six terms are determined from three data sets: detector background, gas background, and sample. The count terms (Cnt) are purely statistical in nature and a derived from simple photo-statics while the 𝜎𝜎2 terms arise from both statistical and systematic effects. All the terms are simplified and are shown to indicate what components are present. This allows one to write the general form for MDC,
( ) ( )( ) ( ) ( )( )
−−−−−
+=
AirAPC
C
BRBRairm
mBq
VTTTTMDC 1000
exp1expexp1*65.471.2 2
03 λλλ
λβγεε
σ
βγ
(9)
where,
( )
airmperXenonofcc.Xenon/ofccVCountsofTimenAcquisitioTGasofTimegocesT
TimeCollectionXenonTtLnλ
RatioBranchingββRatioBranchingγγ
EfficiencyβεEfficiencyγε
LσMemoryCntσceCntInterferenσBckCntσ
Air
A
P
C
BR
BR
β
γ
CMemoryCntceCntInterferenBckCnt
3
2220
0870
sinPr
221
=========
=+++++=
The first term (red) in (9) contains the nuclear physics that pertains directly to the detector. The second term (orange) takes into account the radioactive decay of the particular nucleus. Contained in the second
term is )exp(1
*
C
C
TT
λλ
−−, which is a saturation term. It represents the collection of the radioactive sample
8
from the atmosphere. The collection is assumed to be constant activity collected in a linear fashion. In systems that use a pre-collected sample the second term goes to 1. TC is the collection of the radioxenon in the sphere, while TP is the time from collection stop to detector acquisition start. The TA term is the
acquisition time of the sample. The last term (yellow) converts the rate into the proper units, 3mmBq .
Regions of Interest (ROI) The three data sets can be further broken down into what the data is comprised. The sample file contains the data from the sample plus memory plus ambient background. The gas background contains the memory effect from the previous runs and the ambient background. Finally, the detector background should contain only the ambient background.
The seven regions of interest (ROI) are defined by a range in both γ and β energy. The regions are 214Pb (ROI-1), 135Xe (ROI-2), 133Xe (ROI-3), 133Xe (ROI-4), 131mXe (ROI-5), 133mXe (ROI-6), and an exclusion (ROI-7) region (Figure 2). Each region spans in both γ energy range and β energy range. Each region corresponds to an important β-γ signature or combinations of signatures for each isotope. The 214Pb region (ROI-1) contains just radon daughter products and no radioxenon isotopes. The 135Xe (ROI-2) and 133Xe (ROI-3) regions are free from interferences of the other radioxenon isotopes. There is some small contribution (~2%) from Compton scatter from 135Xe into ROI-3, but this contribution has been ignored for the sake of these calculations. Regions 4, 5, 6, and 7 are admixtures of 133Xe, 131mXe and 133mXe. ROI-7 represents a region with maximal possibility of meta-stable (131mXe and 133mXe) interference while ROI-4 minus ROI-7 represents a pure 133Xe signature.
Figure 2: Placement of the 7 regions of interest (ROI).
9
Ratios of the ROIs account for interference from Radon daughters (Figure 3) as well as the two metastables. There are ratios taken between ROI-1 and the six other ROI (1:2, 1:3, 1:4, 1:5 1:6, and 1:7). The radon daughter ratios are important since they cause interference with 135Xe, 133Xe, 133mXe, and 131mXe. The counts due to the interference are subtracted out. Using a pure spike of radon (daughter products 214Pb and 214Bi) allows the determination of the interference ratios for each of the ROI’s. For the radon, the ratios are taken between ROI-1 and the six other ROI (1:2, 1:3, 1:4, 1:5 1:6, and 1:7). The other important interference ratios are based on 133Xe (Figure 4) in the ROI’s of the two metastables. Here the ratios are 3:4, 3:5, 3:6, 3:7, and 3:(4-7). The 3:4 ratio is important for the case where there are no metastables. The 3:5 and 3:6 ratios are important when there are metastables present. Finally, the 3:7 and 3:(4-7) are important for determining if there are metastables present at all. The last interference term is 135Xe, which uses the ratios of ROI-2 to all lower ROI’s. The 135Xe ratios account for Compton scatter and the ~30 keV x-ray/β coincidence that interferes with ROI-4 and -6. For all of the following calculations it is critical to subtract out the interference terms using the appropriate ratio.
Figure 3: A radon spike used to determine interference ratios with the ROI’s overlaid.
10
Figure 4: 135Xe spike used for determination of 133Xe ROI ratios with ROI’s overlaid. The upper right figure is an expanded view of the lower left section.
LC Calculation The first step taken in the analysis is to correct for dead time. The dead-time is corrected by taking a ratio of the real-time (RT) to live-time (LT).
D
DROInRawROInRaw LT
RTBkgdD *:: =
(10)
ROInRawD
DD Bkgd
LTRT
ROInRaw :*:
=σ
(11)
G
GROInRawROInRaw LT
RTGasG *:: =
(12)
ROInRawG
GG Gas
LTRT
ROInRaw :*:
=σ
(13)
S
SROInRawROInRaw LT
RTSamS *:: =
(14)
ROInRawS
SS Sam
LTRT
ROInRaw :*:
=σ
(15)
11
Subtract the detector background from both the sample and gas background. The sample is composed of ambient background, memory effects from previous samples, and the actual sample of interest. The gas background data (Figure 5) is composed of ambient background and the memory effect from previous samples. The detector background data is composed of only the ambient background (Figure 6). The detector background is measured during the first three days of operation of the system at a new site.
Figure 5: A gas background after a medical isotope (133Xe, 131mXe) spike with ROI’s overlaid.
Figure 6: An example of a detector background data set with ROI’s overlaid.
12
By subtracting, the detector background from the gas background (sample) the data set is reduced to only containing the memory effect (memory and sample). Each file used in the calculation accounts for different periods; for example, the Automated Radioxenon Sampler/ Analyzer (ARSA) uses 72-hrs for a detector background, 8-hours for a typical gas background and 24-hours for a typical sample. The detector background will be normalized to real-time acquisition interval (∆TS, ∆TG, and ∆TD) from which it will be subtracted.
D
SROInRawSROIn T
TDD∆∆
= *:
(16)
ROInRawD
SD D
TT
SROIn :*∆∆
=σ
(17)
D
GROInRawGROIn T
TDD∆∆
= *:
(18)
ROInRawD
GD D
TT
GROIn :*∆∆
=σ
(19)
An example of the three times: ∆TS, ∆TG and ∆TD along with decay of the four primary radioxenon isotopes is depicted in Figure 7. Once the data sets have been time adjusted to same time interval as the sample, the ROI time corrected detector counts, (16), is subtracted from the respective ROI in both the time corrected gas background and sample data sets as seen in (20) and (22).
SROInRawROInROIn DSS −= (20)
22: SROInROInRawROIn DSS σσσ +=
(21)
GROInROInRawROIn DGG −= : (22)
22: GROInROInRawROIn DGG σσσ +=
(23)
The use of a long detector-background count time is important to minimize the uncertainties associated with this measurement, i.e. longer counts times give smaller relative uncertainties.
13
Figure 7: Shows the chemistry timeline (vertical colored bands), detector acquisition (top timeline), and an example of the isotope activity (given by the four lines in the bottom of the figure) present in a typical radioxenon system. In currently developed systems the measurement is corrected to a To of collection stop. The detector background (the section marked with a green horizontal bar) is the first data collected, which on this scale is too small to be displayed. The four regions: white, orange, yellow, and light blue show the number of decays at a given time. The white region (background) contains only decays from the ambient background and gas background (memory effect). The orange region (collection) assumes a linear increase in the number on radioxenon present, so there are an increasing number of decays as one goes forward in time. The yellow region (processing) represents the time between collection and data acquisition, so there is no added radioxenon and only decay. In the last region, light blue (acquisition), there is only decay of the radioxenon present. The top timeline shows what stage of acquisition the detector is in during any given chemistry stage of the system. Another source of uncertainty in the measurement is from interference from one isotope to another. This can be in the form of radon or xenon. Radon interference must be subtracted from both the sample and gas background. This is done, in the case of radon, by using the ratio counts from ROI-1 and then subtract from the corresponding ROI. For the cases where 133Xe is an interference term, the ratio counts from ROI-3 are subtracted from the corresponding ROI. It is worth noting that in cases where there is either no radon or no xenon interference these terms will be zero within statistical uncertainties (i.e. Ratio = 0 and σratio = 0). Of further importance is the need to subtract the gas background, detector background, and interference terms from ROI-3 before using the ratio of ROI-3 as an interference term for other regions.
nROIS RatioSceInterferenRn :11 *= (24)
2:1
2221 **
1:1 nSRatioROIceInterferen RatioSROInRnS
σσσ +=
(25)
( ) nROIROIS RatioRatioSSceInterferenXe :22:112 **
135−= (26)
( ) ( ) 2:2
22222:112 2:2135 nceInterferenSRatioROIROIceInterferen RatioRatioSS
RnSROInXeS⋅++⋅⋅−= σσσσ
(27)
( ) nSSROIS RatioceInterferenceInterferenSceInterferenRnXeXe :33 *
135133−−= (28)
( ) ( ) 2:3
222223 1353:3135133 nceInterferenceInterferenSRatioSSROIceInterferen RatioceInterferenceInterferenS
RnSXeSROInRnXeXeS⋅+++⋅−−= σσσσσ
(29)
14
RnXeXeROIn SSSROInCorrected ceInterferenceInterferenceInterferenSS −−−=135133 (30)
2222133135 XeSXeSRnSROInROInCorrected ceInterferenceInterferenceInterferenSS σσσσσ +++=
(31)
nROIS RatioGceInterferenRn :11 *= (32)
2:1
2221 **
1:1 nGRatioROIceInterferen RatioGROInRnG
σσσ +=
(33)
( ) nROIROIG RatioRatioGGceInterferenXe :22:112 **
135−= (34)
( ) ( ) 2:2
22222:112 2:2135 nceInterferenGRatioROIROIceInterferen RatioRatioGG
RnGROInXeG⋅++⋅⋅−= σσσσ
(35)
( ) nGGROIG RatioceInterferenceInterferenGceInterferenRnXeXe :33 *
135133−−= (36)
( ) ( ) 2:3
222223 1353:3135133 nceInterferenceInterferenGRatioGGROIceInterferen RatioceInterferenceInterferenS
RnGXeGROInRnXeXeG⋅+++⋅−−= σσσσσ
(37)
RnXeXeROIn GGGROInCorrected ceInterferenceInterferenceInterferenGG −−−=135133 (38)
2222133135 XeGXeGRnGROInROInCorrected ceInterferenceInterferenceInterferenGG σσσσσ +++=
(39)
Note that both the number of counts in ROI-1 and the uncertainty of the appropriate ratio (Ratio1:n) contribute to the uncertainty in the interference term. While the statistical uncertainty related to the number of counts in the gas background and the sample is determined from the square root of the counts and hence is variable and can be large in both relative terms and absolute terms, the uncertainty associated with the ratio can be made to be small during calibration. By using a high activity sample, several 10’s to 100’s of counts per second, it is possible to have the ratio uncertainty less than 0.5%.
An additional note is the inclusion of a switch that allows the operator to turn on or off the use of the radon ratio’s and hence radon subtraction. While it was felt at discussions during the Stockholm Noble Gas workshop of 2005 that there should be no option to turn the radon subtraction on and off via Lc calculations or through the use of an operator controlled switch, there are systems that have shown no radon interferences. Because such a system would be penalized in both the uncertainties and the MDC values for the inclusion of the radon ratio it has been determined that an operator controlled switch should be allowed, but no internal switch determined by an Lc calculation should be allowed. It is also important to note that, with careful determination of the radon ratios, the inclusion of radon should have less than a 2% absolute effect on the concentrations, uncertainties, and MDC values.
Continuing with the determination of the concentration and associated uncertainty, subtract the gas background from the sample. Since the gas background is a measure of any residual isotopes present
15
from previous samples, the gas background (Eq. 34) needs to be half-life corrected (See Figure 7 for example decay curves) for each ROI.
( )Sn
Gn
on
ROIn TT
tCorrected
ROInG ee
eGMemory ∆−
∆−
∆−
−−
= **: 1
1* λ
λ
λ
(40)
( )Sn
Gn
on
ROInCorrected
ROInG
TT
tG
Memory ee
e∆−
∆−
∆−
−−
= ** 1
1
*:
λλ
λσσ (41)
Where,
( ) ( )start timen acquisitio Gas-start timen acquisitio Samplet o =∆
n timeacquisitio background GasT G =∆
n timeacquisitio SampleT S =∆
constantdecay Isotope n =λ
At this point, it is possible to calculate LC for both the detector background, interference term, and gas background. Detector LC is simply
2ROInDet DROIno D σσ +=
(42)
2:
2: :: sXeSRnceInterferen ceInterferenSXeceInterferenSRno ceInterferenceInterferen σσσ +++=
(43)
while, GCL is
2: :ROInGG MemoryROInGo Memory σσ +=
(44)
For the definition of σo, see equations (7) and (8).
2222ceInterferenGD oooo σσσσ ++=
(45)
The MDC is calculated for each ROI using (44) and the base (9).
( ) ( )( ) ( ) ( )( )
−−−−−
+=
AirAPC
Coairm
mBq
VTTTT
BRBRMDC 1000
exp1expexp1*65.471.2 2
3 λλλλ
εεσ
βγβγ (46)
At this point, subtract the gas-background half-life corrected counts from the corresponding sample ROI counts (see (30) and (40)).
16
ROInGCorrectedf MemorySSROInROIn :−= (47)
22:ROInGROInCorrectedROInf MemorySS σσσ += (48)
The concentration is calculated for each given ROI using equation (49).
( ) ( )( ) ( ) ( )( ) ,1000*exp1expexp1
2
3
Air
C
APCBRBR
f
airmmBq
VT
TTTS
ionConcentrat ROIn
λλλλ
βγεε βγ −−−−−= (49)
( )222222
*3
+
+
+
+
+
=
Air
V
BRBRf
S
airmmBq
VSionConcentratError AirBRBR
ROIn
ROInfσ
γσ
βσ
ε
σ
ε
σσ γβ
β
ε
γ
ε βγ
(50)
Specific Cases
135Xe
Figure 8: A sample file in which 135Xe is present.
( ) ( )( )( ) ( ) ( )( ) Air
C
AXe
PXe
CXe
Xe
BRBR
Xe
airmmBq
MDC VT
TTTXe 1000*
exp1expexp129.371.2
135135135
2135135250135
3 λλλλ
βγεεσ
βγ −−−−−+
= (51)
σ135Xe is calculated using Eq. 8 where the only interference occurs with radon.
17
( ) ( ) ( )22142214135214
2135135 ***2 135214
PbRatio
PbSamCnt
XePb
XeBckCnt
Xe SamCntsRatio XePb
σσσσ ++= (52)
Where,
2:)(135
ROISamGasXe
BckCnt Counts=σ (53)
In this case, it is assumed that the uncertainties in timing and half-life are negligible. In addition, the half-life correction of the previous 135Xe is ignored since it has less than a 0.8% contribution.
352214352214214 PbPbPbSamCnt SamCntsBckCnts +=σ (54)
Furthermore, the interference term should only include radon interferences, so eq. 39 simplifies.
133Xe
Figure 9: A sample file in which 133Xe is present.
For 133Xe, there are two ROI, 3 and 4. ROI-3 has the events with the 81-keV γ-ray in coincidence, while ROI-4 has the 30-keV x-ray in coincidence. ROI-4 also has two potential interference terms from the 131mXe and 133mXe. The MDC for the 81-keV ROI is calculated the same as 135Xe, discussed in the previous section.
18
AirVCT
ATXePTXe
CTXe
Xe
BRBR
Xe
airm
mBqMDCXe
1000*
133exp1133exp133exp1
21338113329.371.23
81133
−−
−
−−
+=
λλλ
λ
βγβεγεσ
(55)
Where,
( ) ( ) ( )2792142792148113379214
28113381133 ***2 8113379214
PbRatio
PbSamCnt
XePb
XeBckCnt
Xe SamCntsRatio XePb
σσσσ ++= (56)
,
and
8113381133 XeXeBckCnt BckCnts=σ (57)
35221432521479214 PbPbPbSamCnt SamCntsBckCnts +=σ (58)
However, the MDC for the 30-keV ROI is calculated two ways. The first is the same as the 81-keV ROI, because the metastable states are assumed to be missing (uses the entire ROI-4). The second method uses only the sections of ROI-4 that do not overlap with the exclusion region (ROI-7).
( )2Xe3013330133 *2 BckCntXe σσ = (59)
Where,
133Xe30133Xe30BckCnt BckCnts=σ (60)
and the MDC is:
( ) ( )( )( ) ( ) ( )( ) Air
C
AXe
PXe
CXe
Xe
BRBR
Xe
airmmBq
MDC VT
TTTXe 1000*
exp1expexp129.371.2
133133133
21333013330133
3 λλλλ
βγεεσ
βγ −−−−−+
= (61)
The two MDC calculations made for 133Xe can be combined to produce a single MDC for each spectrum. The equation,
( )( ) ( ) 230133281133
133 13 −−
+=
keVMDC
keVMDC
airmmBq
MDCXeXe
Xe
(62)
is the weighted average of the uncertainties and is dominated by the smaller of the two MDC calculations. It should be noted that the equation used above is not mathematically rigorous, but within 10% of the rigorous value.
19
131mXe
Figure 10: A sample file in which 131mXe is present. For 131mXe, the interference terms are due to 133Xe.
5:3ROIROI30131 *
35RatioCntCntSamCnts mXe −= (63)
( ) ( ) ( )23
25:3
2ROI530131 ***25:33 ROIRatioCntBckCnt
mXe CntRatioROI
σσσσ ++= (64)
Where,
ROI5ROI5 BckCntsBckCnt =σ and
ROI3ROI34
BckCntsSamCntsROICnt +=σ (65)
The MDC is then:
( )( )( ) ( ) ( )( ) Air
C
AmXe
PmXe
CmXe
mXe
BRBR
mXe
airmmBq
MDCm
VT
TTTXe 1000*
exp1expexp129.371.2
131131131
21313013130131
3 λλλλ
βγεεσ
βγ −−−−−
+=
(66)
Similarly, 133mXe is done in the same fashion. In this case ROI-6 is used instead of ROI-5.
20
Conclusion Concentration with uncertainty and MDC calculations can be very complex, however with some assumptions they can be simplified considerably without significant impact on the uncertainty of the calculation. In the case beta-gamma radioxenon systems it is very important to account for ambient background, memory effect, and interference. These different components are obtained by different combinations of the three data files: detector background, gas background, and sample. In the end, to obtain the most accurate results it is very important to have a well characterized detector.